Architecture

What Is The Gcf Of 55 And 77, Greatest Common Factor (Gcf) Of 55 And 77

GCF of 55 and 77 is the largest possible number that divides 55 and 77 exactly without any remainder. The factors of 55 and 77 are 1, 5, 11, 55 and 1, 7, 11, 77 respectively. There are 3 commonly used methods to find the GCF of 55 and 77 – prime factorization, long division, and Euclidean algorithm.

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 1 GCF of 55 and 77 2 List of Methods 3 Solved Examples 4 FAQs

Answer: GCF of 55 and 77 is 11.

Explanation:

The GCF of two non-zero integers, x(55) and y(77), is the greatest positive integer m(11) that divides both x(55) and y(77) without any remainder.

The methods to find the GCF of 55 and 77 are explained below.

Listing Common FactorsLong Division MethodPrime Factorization Method

GCF of 55 and 77 by Listing Common Factors

Factors of 55: 1, 5, 11, 55Factors of 77: 1, 7, 11, 77

There are 2 common factors of 55 and 77, that are 1 and 11. Therefore, the greatest common factor of 55 and 77 is 11.

GCF of 55 and 77 by Long Division

GCF of 55 and 77 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (55) by the remainder (22).Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (11) is the GCF of 55 and 77.

GCF of 55 and 77 by Prime Factorization

Prime factorization of 55 and 77 is (5 × 11) and (7 × 11) respectively. As visible, 55 and 77 have only one common prime factor i.e. 11. Hence, the GCF of 55 and 77 is 11.

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GCF of 55 and 77 Examples

Example 1: Find the greatest number that divides 55 and 77 exactly.

Solution:

The greatest number that divides 55 and 77 exactly is their greatest common factor, i.e. GCF of 55 and 77.⇒ Factors of 55 and 77:

Factors of 55 = 1, 5, 11, 55Factors of 77 = 1, 7, 11, 77

Therefore, the GCF of 55 and 77 is 11.

Example 2: For two numbers, GCF = 11 and LCM = 385. If one number is 77, find the other number.

Solution:

Given: GCF (x, 77) = 11 and LCM (x, 77) = 385∵ GCF × LCM = 77 × (x)⇒ x = (GCF × LCM)/77⇒ x = (11 × 385)/77⇒ x = 55Therefore, the other number is 55.

Example 3: Find the GCF of 55 and 77, if their LCM is 385.

Solution:

∵ LCM × GCF = 55 × 77⇒ GCF(55, 77) = (55 × 77)/385 = 11Therefore, the greatest common factor of 55 and 77 is 11.

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FAQs on GCF of 55 and 77

What is the GCF of 55 and 77?

The GCF of 55 and 77 is 11. To calculate the GCF (Greatest Common Factor) of 55 and 77, we need to factor each number (factors of 55 = 1, 5, 11, 55; factors of 77 = 1, 7, 11, 77) and choose the greatest factor that exactly divides both 55 and 77, i.e., 11.

How to Find the GCF of 55 and 77 by Long Division Method?

To find the GCF of 55, 77 using long division method, 77 is divided by 55. The corresponding divisor (11) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 55, 77?

The following equation can be used to express the relation between LCM and GCF of 55 and 77, i.e. GCF × LCM = 55 × 77.

What are the Methods to Find GCF of 55 and 77?

There are three commonly used methods to find the GCF of 55 and 77.

By Listing Common FactorsBy Prime FactorizationBy Long Division

If the GCF of 77 and 55 is 11, Find its LCM.

GCF(77, 55) × LCM(77, 55) = 77 × 55Since the GCF of 77 and 55 = 11⇒ 11 × LCM(77, 55) = 4235Therefore, LCM = 385☛ Greatest Common Factor Calculator

How to Find the GCF of 55 and 77 by Prime Factorization?

To find the GCF of 55 and 77, we will find the prime factorization of the given numbers, i.e. 55 = 5 × 11; 77 = 7 × 11.⇒ Since 11 is the only common prime factor of 55 and 77. Hence, GCF (55, 77) = 11.☛ What is a Prime Number?